Bayesian Active Learning for Censored Regression

Frederik Boe Hüttel; Christoffer Riis; Filipe Rodrigues; Francisco Pereira

doi:10.1007/978-3-032-05981-9_3

Bayesian Active Learning for Censored Regression

Frederik Boe Hüttel
, Christoffer Riis
, Filipe Rodrigues^*
, Francisco Pereira

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

Bayesian active learning is based on information theoretical approaches that focus on maximising the information that new observations provide to the model parameters. This is commonly done by maximizing the Bayesian Active Learning by Disagreement (BALD) acquisition function. However, it is challenging to estimate BALD when the new data points are subject to censorship, where only clipped values of the targets are observed. To address this, we derive the entropy and the mutual information for right-censored distributions and derive the BALD objective for active learning in censored regression (C-BALD). We propose a novel modeling approach to estimate the C-BALD objective and use it for active learning in the censored setting. Across a wide range of datasets and models, we demonstrate that C-BALD outperforms other Bayesian active learning methods in censored regression.

Original language	English
Title of host publication	Machine Learning and Knowledge Discovery in Databases. Research Track - European Conference, ECML PKDD 2025, Proceedings
Publisher	Springer Science and Business Media Deutschland GmbH
Publication date	2026
Pages	36-51
ISBN (Print)	9783032059802
DOIs	https://doi.org/10.1007/978-3-032-05981-9_3
Publication status	Published - 2026
Event	European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2025 - Porto, Portugal Duration: 15 Sept 2025 → 19 Sept 2025

Conference

Conference	European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2025
Country/Territory	Portugal
City	Porto
Period	15/09/2025 → 19/09/2025

Series	Lecture Notes in Computer Science
Volume	16014 LNCS
ISSN	0302-9743

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

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10.1007/978-3-032-05981-9_3

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title = "Bayesian Active Learning for Censored Regression",

abstract = "Bayesian active learning is based on information theoretical approaches that focus on maximising the information that new observations provide to the model parameters. This is commonly done by maximizing the Bayesian Active Learning by Disagreement (BALD) acquisition function. However, it is challenging to estimate BALD when the new data points are subject to censorship, where only clipped values of the targets are observed. To address this, we derive the entropy and the mutual information for right-censored distributions and derive the BALD objective for active learning in censored regression (C-BALD). We propose a novel modeling approach to estimate the C-BALD objective and use it for active learning in the censored setting. Across a wide range of datasets and models, we demonstrate that C-BALD outperforms other Bayesian active learning methods in censored regression.",

author = "H{\"u}ttel, \{Frederik Boe\} and Christoffer Riis and Filipe Rodrigues and Francisco Pereira",

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series = "Lecture Notes in Computer Science",

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Hüttel, FB, Riis, C, Rodrigues, F & Pereira, F 2026, Bayesian Active Learning for Censored Regression. in Machine Learning and Knowledge Discovery in Databases. Research Track - European Conference, ECML PKDD 2025, Proceedings. Springer Science and Business Media Deutschland GmbH, Lecture Notes in Computer Science, vol. 16014 LNCS, pp. 36-51, European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2025, Porto, Portugal, 15/09/2025. https://doi.org/10.1007/978-3-032-05981-9_3

Bayesian Active Learning for Censored Regression. / Hüttel, Frederik Boe; Riis, Christoffer; Rodrigues, Filipe et al.
Machine Learning and Knowledge Discovery in Databases. Research Track - European Conference, ECML PKDD 2025, Proceedings. Springer Science and Business Media Deutschland GmbH, 2026. p. 36-51 (Lecture Notes in Computer Science, Vol. 16014 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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AU - Hüttel, Frederik Boe

AU - Riis, Christoffer

AU - Rodrigues, Filipe

AU - Pereira, Francisco

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N2 - Bayesian active learning is based on information theoretical approaches that focus on maximising the information that new observations provide to the model parameters. This is commonly done by maximizing the Bayesian Active Learning by Disagreement (BALD) acquisition function. However, it is challenging to estimate BALD when the new data points are subject to censorship, where only clipped values of the targets are observed. To address this, we derive the entropy and the mutual information for right-censored distributions and derive the BALD objective for active learning in censored regression (C-BALD). We propose a novel modeling approach to estimate the C-BALD objective and use it for active learning in the censored setting. Across a wide range of datasets and models, we demonstrate that C-BALD outperforms other Bayesian active learning methods in censored regression.

AB - Bayesian active learning is based on information theoretical approaches that focus on maximising the information that new observations provide to the model parameters. This is commonly done by maximizing the Bayesian Active Learning by Disagreement (BALD) acquisition function. However, it is challenging to estimate BALD when the new data points are subject to censorship, where only clipped values of the targets are observed. To address this, we derive the entropy and the mutual information for right-censored distributions and derive the BALD objective for active learning in censored regression (C-BALD). We propose a novel modeling approach to estimate the C-BALD objective and use it for active learning in the censored setting. Across a wide range of datasets and models, we demonstrate that C-BALD outperforms other Bayesian active learning methods in censored regression.

U2 - 10.1007/978-3-032-05981-9_3

DO - 10.1007/978-3-032-05981-9_3

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T3 - Lecture Notes in Computer Science

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BT - Machine Learning and Knowledge Discovery in Databases. Research Track - European Conference, ECML PKDD 2025, Proceedings

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Hüttel FB, Riis C, Rodrigues F , Pereira F. Bayesian Active Learning for Censored Regression. In Machine Learning and Knowledge Discovery in Databases. Research Track - European Conference, ECML PKDD 2025, Proceedings. Springer Science and Business Media Deutschland GmbH. 2026. p. 36-51. (Lecture Notes in Computer Science, Vol. 16014 LNCS). doi: 10.1007/978-3-032-05981-9_3

Bayesian Active Learning for Censored Regression

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